Related papers: Functional moderate deviations for triangular arra…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.
The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…
In this paper we establish a moderate deviation principle of the hitting times for trajectories of sums of independent and identically distributed random variables. The main idea of proof is to convert the moderate deviations over a small…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Suppose $ E$ is a space with a null-recurrent Markov kernel $ P$. Furthermore, suppose there are infinite particles with variable weights on $ E$ performing a random walk following $ P$. Let $ X_{t}$ be a weighted functional of the position…
When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…
We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization…
We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and…
In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied…
The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be…
Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the $\beta$-mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical…
Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schr\"odinger type equation with linear drift term and noise driven by a $Q$-Wiener process. The central limit theorem is also shown for the equation…
We give a simple and general central limit theorem for a triangular array of m-dependent variables. The result requires only a Lindeberg condition and avoids unnecessary extra conditions that have been used earlier. The result applies also…
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…